论文标题
平衡状态对应于靶向超平均非平衡对统计
Equilibrium States Corresponding to Targeted Hyperuniform Nonequilibrium Pair Statistics
论文作者
论文摘要
张刺山猜想[Phys。 Rev. E 101, 032124 (2020)] states that any realizable pair correlation function $g_2({\bf r})$ or structure factor $S({\bf k})$ of a translationally invariant nonequilibrium system can be attained by an equilibrium ensemble involving only (up to) effective two-body interactions.为了测试这一猜想，我们考虑了两个近期兴趣的单数非平衡模型，这些模型也具有异国情调的超均匀性特性：2D“完美玻璃”和一个3D关键的吸收态模型。我们发现，具有有效的一体和两体电位的平衡状态可以准确地实现每个非平衡目标，从而为猜想提供了进一步的支持。为了表征这种非平衡对应关系的结构退化，我们计算了这两个模型的高阶统计数据，以及对于高均匀随机晶格（URL）的高均匀统计的统计，其高阶统计数据可以非常精确地确定。有趣的是，我们发现，通过“孔”概率分布衡量，具有匹配对统计的非平衡系统和平衡系统之间的高阶统计数据的差异提供了超出均衡程度的度量。我们表明，所研究的所有三个系统都具有\ textIt {有界孔}属性，并且在URL中最大孔大小的孔比基础简单的立方晶格中的孔要稀有得多。值得注意的是，与目标对应物相比，在淬火后，所有三个系统的有效电位具有更强的超均匀性形式。预计我们的工作将促进可调超一样式软性系统的自组装。
The Zhang-Torquato conjecture [Phys. Rev. E 101, 032124 (2020)] states that any realizable pair correlation function $g_2({\bf r})$ or structure factor $S({\bf k})$ of a translationally invariant nonequilibrium system can be attained by an equilibrium ensemble involving only (up to) effective two-body interactions. To test this conjecture, we consider two singular nonequilibrium models of recent interest that also have the exotic hyperuniformity property: a 2D "perfect glass" and a 3D critical absorbing-state model. We find that each nonequilibrium target can be achieved accurately by equilibrium states with effective one- and two-body potentials, lending further support to the conjecture. To characterize the structural degeneracy of such nonequilibrium-equilibrium correspondence, we compute higher-order statistics for both models, as well as those for a hyperuniform 3D uniformly randomized lattice (URL), whose higher-order statistics can be very precisely ascertained. Interestingly, we find that the differences in the higher-order statistics between nonequilibrium and equilibrium systems with matching pair statistics, as measured by the "hole" probability distribution, provides measures of the degree to which a system is out of equilibrium. We show that all three systems studied possess the \textit{bounded-hole} property, and that holes near the maximum hole size in the URL are much rarer than those in the underlying simple cubic lattice. Remarkably, upon quenching, the effective potentials for all three systems possess local energy minima with stronger forms of hyperuniformity compared to their target counterparts. Our work is expected to facilitate the self-assembly of tunable hyperuniform soft-matter systems.
